Exploratory multivariate data analysis

Dijksterhuis, G. B. and Reiser, W. J. (1995). The role of permutation tests in exploratory multivariate data analysis. Food Quality and Preference, 6, 263-270. 

Husson, R, Josse, J., Le, S. and Pages, J. (2008, Fehruary 21). FactoMineR Exploratory Multivariate Data Analysis with R. Retrieved Fehmary 05, 2014, from http //factominer. free.fr/index.html. 

Other methods consist of algorithms based on multivariate classification techniques or neural networks they are constructed for automatic recognition of structural properties from spectral data, or for simulation of spectra from structural properties [83]. Multivariate data analysis for spectrum interpretation is based on the characterization of spectra by a set of spectral features. A spectrum can be considered as a point in a multidimensional space with the coordinates defined by spectral features. Exploratory data analysis and cluster analysis are used to investigate the multidimensional space and to evaluate rules to distinguish structure classes. 

Spectral features and their corresponding molecular descriptors are then applied to mathematical techniques of multivariate data analysis, such as principal component analysis (PCA) for exploratory data analysis or multivariate classification for the development of spectral classifiers [84-87]. Principal component analysis results in a scatter plot that exhibits spectra-structure relationships by clustering similarities in spectral and/or structural features [88, 89]. 

Exploratory data analysis has the aim to learn about the data distribution (clusters, groups of similar objects). In multivariate data analysis, an X-matrix (objects/samples characterized by a set of variables/measurements) is considered. Most used method for this purpose is PCA, which uses latent variables with maximum variance of the scores (Chapter 3). Another approach is cluster analysis (Chapter 6). 

Principal component analysis (PCA) can be considered as the mother of all methods in multivariate data analysis. The aim of PCA is dimension reduction and PCA is the most frequently applied method for computing linear latent variables (components). PCA can be seen as a method to compute a new coordinate system formed by the latent variables, which is orthogonal, and where only the most informative dimensions are used. Latent variables from PCA optimally represent the distances between the objects in the high-dimensional variable space—remember, the distance of objects is considered as an inverse similarity of the objects. PCA considers all variables and accommodates the total data structure it is a method for exploratory data analysis (unsupervised learning) and can be applied to practical any A-matrix no y-data (properties) are considered and therefore not necessary. 

We have previously underlined that the absence of a common linear intensity axis (spectra not properly normalized) would lead to erroneous predictions in quantitative spectral analyses and in meaningless interpretations for exploratory data analyses. Another prerequisite for multivariate data analysis is that the data conform to the selected model. An assumption that applies to most of the multivariate methods is that the data are low rank bilinear. For most multivariate methods, this implies that the spectral axis must remain constant, that is, the signal(s) for a given chemical compound must appear at the same position in all the spectra. We will see how a different interval-based approach, not aimed at building chemometric models, but rather at spectral data preprocessing can effectively contribute to achieve an efficient and comprehensive horizontal signal alignment. 

Multivariate analytical images may be processed additionally by chemo-metrical procedures, e.g., by exploratory data analysis, regression, classifica-tion> and principal component analysis (Geladi et al. [1992b]). 

We will skip (1) and (2) above as methods not to be preferred as global analyses. Graphical displays have tremendous values as exploratory data analysis (EDA) techniques with the type of data one encounters in these studies. For formal analyses, one could weigh univariate repeated and other factorial designs against their true multivariate counterparts. 

Exploratory data analysis (3 ) is performed on the data base using multivariate statistical techniques. The objectives of... 

From an analytical viewpoint, statistical approaches can be subdivided into two types Exploratory Data Analysis (EDA) and Confirmatory Data Analysis (CDA). Exploratory data analysis is concerned with pictorial methods for visualising data shape and for looking for patterns in multivariate data. It should always be used as a precursor for selection of appropriate statistical tools to confirm or quantify, which is the province of confirmatory data analysis. CDA is about applying specific tools to a problem, quantifying underlying effects and data modelling. This is the more familiar area of statistics to the analytical community. 

The most important method for exploratory analysis of multivariate data is reduction of the dimensionality and graphical representation of the data. The mainly applied technique is the projection of the data points onto a suitable plane, spanned by the first two principal component vectors. This type of projection preserves (in mathematical terms) a maximum of information on the data structure. This method, which is essentially a rotation of the coordinate system, is also referred to as eigenvector-projection or Karhunen-Loeve- projection (ref. 8). 

EIN SIGHT Infometrix, 2200 Sixth Ave. 833, Seattle, Wash. 98121, USA 300. Exploratory analysis of multivariate data, graphics-oriented (ref. 18). 

The main goal of this section is to provide a summary of several of the most widely used multivariate procedures in food authentication out of the vast array currently available. These are included in well-known computer packages such as BMDP, IMSL, MATLAB, NAG, SAS, SPSS and STATISTIC A. The first three subsections describe unsupervised procedures, also called exploratory data analysis, that can reveal hidden patterns in complex data by reducing data to more interpretable information, to emphasize the natural grouping in the data and show which variables most strongly influence these patterns. The fourth and fifth subsections are focused on the supervised procedures of discriminant analysis and regression. The former produces good information when applied under the strictness of certain tests, whereas the latter is mainly used when the objective is calibration. 

Data sets can be analyzed by exploratory data analysis, usually based on multivariate techniques, such as principal component analysis cluster analysis allows the evaluation of... 

In the first mentioned type of application, electrophoretic data are subjected to exploratory analysis techniques, such as principal component analysis (PCA) (5-8), robust PCA (rPCA) (9-13), projection pursuit (PP) (6,14-18), or cluster analysis (8, 19, 20). They all result in a simple low-dimensional visualization of the multivariate data. As a consequence, it will be easier for the analyst to get insight in the data in order to see whether there is a given... 

Gordon, A. E. (1981). Classification Methods for Exploratory Analysis of Multivariate Data. Chapman and Hall, New York. 

Cluster analysis is justifiably a popular and common technique for exploratory data analysis. Most commercial multivariate statistical software packages offer several algorithms, along with a wide range of graphical display facilities to aid the user in identifying patterns in data. Having indicated that... 

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